Acharge q experiences no net force at a particular point in space. which of the following situations described below must always be true? -there are no other charges nearby. -if there are other charges nearby, they must all have the same sign as q. -if there are other charges nearby, they must all have the opposite sign of q. -if there are other charges nearby, the total positive charge must equal the total negative charge. -none of the above

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.